[bjornsing]

> IMHO what made hard problems difficult to solve is actually the 'intneral structure' of the problems.

20 years ago I wrote a master’s thesis in computer vision. The stereo matching algorithm I developed could be expressed as a big integer linear program. But after pondering it for some time I realized it could also be expressed as a dynamic programming problem, with tiny integer linear programs as subproblems. Reduced the runtime by like a factor of 1000x, or more.

[raverbashing]

Not that uncommon.

I feel most of those big search problems could be solved much easier and quicker with some form of annealing/tree search/dynamic or greedy algorithms with results very close to the theoretical linear optimum

But of course those won't get you a thesis ;)

[bjornsing]

> with results very close to the theoretical linear optimum

In this case I could prove it was the globally optimal solution.

But this was only possible of course due to the internal structure of the problem: it was in effect a simpler problem hiding within a linear integer program. Standard solvers couldn’t find this structure, but it was possible to do by hand.

[hustwindmaple1]

Reformulation is a good strategy for many hard problems.

It might also be possible to add problem-specific cuts/heurstics to the solver so that it can solve it fast.

[djsavvy]

Wow, this sounds interesting! Do you have a link to that thesis?

[bjornsing]

Unfortunately not. It’s on paper and in Swedish only.